Vehicles have been equipped with spike tires or with tire chains for driving ice roads and snow-covered roads. This, however, causes environmental problems such as dust pollution, and studless tires have been developed as the replacement for the spike tires and the tire chains for driving ice roads and snow-covered roads. The studless tires have been improved in their materials and designs for driving snow-covered roads whose surface is rougher than that of usual roads. Specifically, there have been developed rubber compositions which contain diene rubbers having excellent low-temperature properties. Recently, however, the studless tires have been required to achieve further improvement of performance on ice and snow, as well as improvement of abrasion resistance.
Patent Documents 1 to 3 disclose that the following rubbers can improve performance on ice and snow and other performances, and are useful as rubber materials for tire treads. Patent Document 1 discloses a polybutadiene modified by an organoalkoxysilane or the like. Patent Document 2 discloses a polybutadiene modified by a diamine compound. Patent Document 3 discloses a diene rubber modified by a silicon compound having an amino group and an alkoxy group. Patent Documents 4 and 5 disclose that it is possible to improve performance on ice and snow and other performances by blending silica into a diene rubber modified by a silicon compound having an amino group and an alkoxy group, and the rubber compositions thereby produced are useful for tire treads.
However, the studless tires can be further improved in performance on ice and snow and abrasion resistance while reducing strain dependence of hardness of the tread rubbers for the studless tires and maintaining rigidity on roads that are not covered with snow.    Patent Document 1: JP 2001-40001 A    Patent Document 2: JP 2007-31722 A    Patent Document 3: JP 2000-159814 A    Patent Document 4: JP 2000-344954 A    Patent Document 5: JP 2000-344955 A